标题： 超对称与迹公式 III. 弗伦克尔迹公式 显示英文标题

标题： Supersymmetry and trace formulas III. Frenkel trace formula

摘要： 通过应用在\cite{Choi:2021yuz,Choi:2023pjn}中引入的新的超对称局域化原理，我们提出了两种互补的方法来推导半单紧李群$G$的“非手征”迹公式，该公式推广了所谓的弗伦克尔迹公式。 每种图景对应的物理系统分别是$G$上的量子力学sigma模型和$G\times G$上的规范sigma模型，这两种方法分别紧密遵循埃斯金迹公式\cite{Choi:2021yuz}和塞尔伯格迹公式\cite{Choi:2023pjn}的精神。 这些方法在\cite{Choi:2021yuz}和\cite{Choi:2023pjn}中的两种看似独立的推导之间提供了自然的概念桥梁。 显示英文摘要

摘要： By applying the new supersymmetric localization principle introduced in \cite{Choi:2021yuz,Choi:2023pjn}, we present two complementary approaches for the path integral derivation of the `non-chiral' trace formula for a semisimple compact Lie group $G$, which generalizes the so-called Frenkel trace formula. Corresponding physical systems for each picture are the quantum mechanical sigma model on $G$ and the gauged sigma model on $G\times G$, and the approaches closely follow the spirit of the Eskin trace formula \cite{Choi:2021yuz} and the Selberg trace formula \cite{Choi:2023pjn} respectively. These methods provide a natural conceptual bridge between two seemingly independent derivations in \cite{Choi:2021yuz} and \cite{Choi:2023pjn}.